Algebra 1 FINAL Exam Review Name:-----''--"'----~'''--'''-___>."d:op;.___----=_.!'''T_--

DUE DATE: _ _ Period: _ Chapter 6 - Solving linear inequalities, graphing linear inequalities 2012-2013

• Number lines • Coordinate planes

Chapter 7 - Solving systems of equations (including word problems) and solving systems of linear inequalities

• Solve by o Substitution o Graphing o Elimination

Chapter 8 - Exponents and Scientific Notation

• Positive exponents

• Negative exponents

Chapter 9 - Polynomials

• Adding • Subtracting • Multiplying

o Distributing o Foil,

• Factoring

Chapter 10 - Graphing quadratic functions

• Parabolas

• Vertex • Axis of Symmetry

• Opening • Width in relation to the parent function y = x 2

Chapter 9 and Chapter 10 - Solving quadratic functions

4~S ~~c; ~ • Solve by

o Factoring Q~~~ o Graphing o Quadratic formula

L\~c;st~~ 'S~ tbChapter 11 (11.2) - Simplifying radicals

Date:

--­

Chapter 12 (12.1) Inverse and direct variation

Polynomials Division (12.3)

• By monomials • By binomials

Chapter 3 (3.8) ­ Solve literal equations

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You will be allowed to use your SOL formula sheet on the Final Exam!

Part 1: Solving inequalities - Directions: Solve each inequality and draw its graph.

1) 7(2 - v) ~ - (v - 8)V~.\ ~~~-t-.-+--+---. IL-\- U~-V Ol2.3

LU IU I

2) 4(x - 3) > 3(x + 4) - 9 X "7IS l\x - -:A /' ?J ---t. -\-YL-~

L\.x -\2... / 3 -X T­-3x ,,'1- -:ox \':J. ­

\ L-&' 3) 2(2b - 1) - 3(b + 1) > 3b + 7 '0 "~=jIiii:~--+----I----+---.

L\'o-) -3b-3 7 6bt-1 '0 -5 73b +-7

-'0 =J -'0 -,

- ~ /aD -;;:~

-l97 D

\ L L\--'2 'X - 0<5) -2 < 2x - 1 :::. 3 \ \

- -\ 0 \ a - \ L~X:::Lt

to. ~ ' ­

-~ LX I- ~ '2.. 6) 9 - 2x > 11 or 9 - 2x :::. -1

-~ -~ ~ -y_I-_-~\ ----..:.......:.---=...'tt":?~__r__r___r___r_........~

Part II: Graphing Linear Inequalities - Directions: Graph the linear inequalities.

7) Y ­

~ ~

o L --3>

t~

Solve the system of linear inequalities.

3 y ~ 4 x ­

9) 3x + y >-3

1 Y :::; ­

Part III:

11) Y '" -- 2x + 2 x-y=4

y

2x .::: - 3 f--t---+---+--+--+--+--t--J-+---+---+--+---.IIII*"-h-+...o.,J

~')( -3 f------I-+--+--+--+---t--+--+-+___+___+_~

Systems of Equations x+y=O

~~ =--..-I--+--+--+-I---1---+--+---1 X

12)

\Solve the systems of equation using th),graphing method. 3x + yy =-8 -!

'"'\

" ,

" ,\ ~

\)< \ '\

"' \ "'\ \ "" x

IS :'\ '\ "-\ r'\

" " r'\ 3"\ r"\ ,

--:J ~

1--t--+--+---+--+---+--+--I----H....l:-~+--+---l-t----1x

f---i-+--+-l--+--+- ---I--+-+----\-+-+-+-+-lF

y

3 !'olo:::-+--+--f---+--\+.T--4'-.:-jq-!:,-f.,-j.-""+''--''h-'"+'--\~+--f'''''''''

2 x + 2 Hr+~-':+-"~~

2 8) y> -"3x + 1

----

~ Solve the systems "Si:(e S,"bSti:)O" method.

x - Sy = 6 13) \ ­

3x - 2y = 5 .

3)( -2~ --=-5 3(5 ~lo)-'2- -:- 5 \S~ ~ -'L~ :. 5

3 +- ~ ~5 -\~ -\R­

~s)( -\l.\y-=-I.\; \.A 'I \~ -\b

3Cfx - ~ -~ ~

X-==--\ 35 -2-h~\S -q - 2-h -:;.- \~

q '1

- '-"" -:::- 2.J-\ ~~-\L-Solve the systems using any method.

17) Sp+12q =13 t-\ 3... J 18) 3Y-6X=24~ . 0:0 ~ri ~ \\1.' .3 (3P + 4q = 3 ' Z- 8+2x=y -D~~

~(.lX+-~) -lox -:0-;)4­5 -\-\L~-=- \3> ~~ -=~ lox ~)l\ -lo X -=-~e C1 ~\lc\.. ~ - - 3 +-1-\ -:. 3- dl\ ~~4-- ~ -.~ 4~~

~;\ ~-~ 4

Part IV: Exponents

Simplify. Give answers in terms of positive exponents:

5 ~i% ~U (19) 1~·~ c,j 20)

;Y~ 3xy·

::,~~20 j

Oi ~~ CL 3a2 ~

23)22) -..;-24ab ~ 8b 2x 3

ic..L I -::: - ~b ~a..D ls>4 r:/. 'C?­C)

<6~ 24) 14x-7 ><7 20) (Z-2 )-3

L..;-(L)32x

_ X le -

\dS 2J3

-~ 5

-1 J2 24) (~: J~ ~

~)~ LX'Y''' 23) (:~22) (;:J

Part v: Polynomials - Directions: Simplify.

25) (7x2-3XY+4y 2)+(2X2-xy_ y 2) Oi x?..- 4xj 'r3~L.-c2<>vL -\-~-L\

Ja.J.+-3~ \4- _;;.;:- ~:~ , L\ct"> + ud- - 1..\.<>-.

1.­

27) (5x - 3)(2x + 1) \ bX - X-3 28) (3t - 2)(4t + 5) \d±£-~Ih- \D -\.R"X +- Sx ~~t \st

29) (x + 2)(x - 5) X 1,.. - 3x -\D 30) (x + 3)(x + 5) X"2-4-8 X + S

31) (c + 2)(c _ 5) ~.J. -~-\ D 32) (2a-1 )(2a2 + 3a - 4)

Part VI' Factoring - Directions: Facr completely.

33) x' - 11x + 28 L~--1'lx-4 34)

235) x + 3x - 54 ()(+~-y 36) x' - 10x - 24 (j. - \'d-J6s.+-~

&-~r3) 38) x'-3x-40 .L,,--ilx\-s) 39) Sy'-16y+3 (Sy¥~-3) 40) 9x

2

41) 3x' + 2x- sL3x.i?tY,- ~ 42) 3x2 + 19x + 6

44) 4x2- 49 (")..'6- Y-~X+--,)

+ 3x - 2 ~~-4---A--~3~+2) +~

Part VII: Graphing quadratic functions,

45) For the~(":O~ j~ 2x' + 1, find all olthe following

a) Vertex: \ b) Opening up or down: '\. !~ ~ \

c) Maximum or minimum: ---'-'-'1...Jl....'~c.=.~=:::.JL..li.........-..J

d) Axis of Symmetry: _~_-==--

e) x-intercepts (solutions}: _-.l~U-----!~~~~""'''''''''''JJ\

f) y-intercept: J b \ \)

g) Narrower, wider or the same as its parent function y = x 2

/,

I \ II

11.'

\,/ ., ..

... " ,

f\ CU\ .T II It

h) Graph:

6

I

\,

I'

J

\

\

\ \ 1 I

-I-H--+-t-+--+--+--+--++--If--++-I-+--+--+-+---1

'\ I

---. ­ ---­ -­ ---t-Hl-+-t---f--il-t-++-t-+--+--t-+----j / --~-+--+--+--+--t-tt\-t-I-+-tt---/+---+--+---H--+-t-H

f----I­ - - ­ -+-+-~~D--+--+--+-I--+--+-I-+-+---I

H---+--+-+--+--+--t-f--t-H---+--+-+--+---H-f-+--I/

I-+--+--+-+--+----H--+---+----I-·-+·-f-+--t-f-+--I-f-+--1

" 1--1­ ·--!-+-I--+--+-I-+-I--I-+--+-+-+-+-II-I­ ' ­

"

'S 'f;-\ :=::=::::-=:=-::--+----II-r--+--t--II---+--t-+---+--t----+-----1

..D \

\ f) y-intercept: ~lo)

f\. tf1 """ \-\r'!l

~WJ'\\.. 1 246) For the function y = - - x - 3, find all of the following:

a) Vertex: CD \-3L b) Opening up or down: •

c) Maximum or minimum: ri"'C'Q.ti}..X!\~

d) Axis of Symmetry: '/... --=-0

f) y-intercept:

g) Narrower, wider or the same as its parent function y = x 2

h) Graph: ~(>< +-3Yx-\) :;),,('1.L.- ~ '-~-3J

47) For the function y = 2X 2 + 4x - 6, find all of the following

a) Vertex: ( -\ \ - ~_ b) Opening up or down:J~ \ \

c) Maximum or minimum: rm\.X'\U'IT'\.~ J

d) Axis of Symmetry: 'A-:::.--\ e) x-intercepts (solutions): X-==-3 I '6:=- \

2g) Narrower, wider or the same as its parent function y = x

h) Graph:

~ ~ _\(,/l.- lJ,)<. -l--S) ~ - - l't ­48) For the function y = - x 2 + 6x - 5 , find all of the following:

a) Vertex: l?) I 4,J-- b) Opening up or down: --===-_ \ \

c) Maximum or minimum: ~~\1~....;;,

d) Axis of Symmetry: >< -=-..3 e) x-intercepts (solutions): X7:- \) Y. -::- 5 f) y-intercept: L() I - s)

2g) Narrower, wider or the same as its parent function y = x S~

h) Graph:

7

Part VII: Solving quadratic equations.

Solve by factoring.

49) x2 -x-6 = 0 X ~ ~\ -"7.­()<- ~i-L):="'O

52) x2 + 9 =10x ;("7-°1 1 \

t L_ \ X ct ':- D

Lx-or Cx-\ -=- D

50) 2x'-5x-3=0 x'=--~\ 3 51) x'+25=10x I< =-5 l~'X ~\'Y.f - '3') '=-D x1-- \D)(-\-dS =-D

(X -s"( )(- 5) =-D

Solve using the quadratic formula. Round answers to the nearest hundredth, if necessary.

Find the value of the discrimant. Then use it to decide how mamy different real-number roots the equation has.

59) x 2 -2x+3=0 -~ 60) 3x2 -8x+2=0 '-\D 61) 9x2 -12x+4=0 D \ t 2J'-- 4(~1 (-'6)'--'-\( :Xl.) (-Il-Y- liectY4 I

L\ - yL \0 - 'dL\- .L\L\- - L\L.\

Part VIII: Radicals - Directions: Simplify the radicals.

63) ~48 L\S3 64) J50 SJ7­A \\p 3 :J'S" '2....

66) J99 3~ 1\ ~ t,

69) 213·13 2·3

74) __

J7f nl(" 77) if40 ~ ~ss- 78) if56

t'\.,. f\ lSS ~7

80) ~ 3 ~J3 81) ~:fif\ 13 5

71.3

fu ~ 1 ~

9

Part IX: Direct and Inverse Variation

Tell whether the equation represents direct variation, inverse variation, or neither

85) xy = -2 86) Y = x 87) Y = 3x-1 4

88) The variables x and y vary inversely, and y =-4 when x = 6. Write an inverse variation equation that relates x and y. Then find the value of y when x = 3. '/... -=- 0.­

\, (-L\')-=-o-' _L'-\~o.-

89) The variables x and y vary inversely, and y =5 when x =-3. Write an inverse variation equation that relates x and y. Then find the value of y when x = 9.

x~ :::-loO 90) Tell whether the oredered pairs {(-20, -3), (-12, -5), (10, 6), (15, 4), (40, 1.5)} represent inverse variation. If so, write the inverse variation equation.

Part X: Polynomial Division - Directions: Simplify!

x-~ x-\ \ '/... l­ _

G )( 1-_ ')(

-~~ +3 -~x +.3 -

I I

-----

1Ox 2- 5x + 15 96) -3x

3- 6x

2 + 12X X1....+;]X - Lt 95) -5 -3x

Part XI: Literal Equations ~f\

1 £.: -::;:;... \,...97) Solve a + by =c for a. ~ -::. e.,.-'oj 98) Solve A = -b'll or h. _'----__-=1.J=__

2

'oj -~

1 . 99) What equation do you obtain when you solve the equation A = -(b1 + b2 )h for b1 ?

2

AC) b =--b D) b = 2A

1 2h 2 1 h-b

x X2

d f1""=- '0 \ +bL-. h

-

11

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